We do it a couple ways in my dojo. I would have to agree with David & Keith though, ask your sensei. Anyway, the two ways we do it in our dojo are

1.) Have both palms up towards the ceiling and rest the tsuka in your left hand and the "blade" resting in your right hand. The bokken should be parrallel to the floor. Make sure the cutting edge of the blade is facing you and don't wrap your fist around the blade. We lightly place our thumbs on the top of the bokken because it is in an imaginary saya (until we draw it). We then either hand it to them or some of us tend to rei slightly and hand it to them.

2.) Hold the bokken like you normally would in your right hand as if you were about to cut. Now, flip the bokken upside down so the tip is pointing at the floor (your hand should be in the same position as it was before) and the blade is now facing your partner. (For the next part, imagine you and your partner are in a square room with one wall to your front, to your back and one on each side.) Rotate your fist so your fingers are pointing down towards the floor, which puts the tip towards the right wall. Then move your fist towards the corner to your front right (about 45 degrees to your right from your partner). They can take the bokken from you without the blade or tip being pointed at them and the blade and tip is also away from you. Hope I explained that well enough for you to understand. HAHA.

~Look into the eyes of your opponent & steal his spirit.
~To be a good martial artist is to be good thief; if you want my knowledge, you must take it from me.